Algebraic expressions · Ages 13–14

What a polynomial is worksheet

Part of: Polynomials & identities

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Algebraic expressions · Ages 13–14

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The degree of the polynomial 6x⁶ + 5x²y² − 10 is .
Answer:
2.The degree of the polynomial 4x⁴ + 7x²y³ − 1 is .
Answer:
3.In the polynomial 4x³ − x² + x + 19, the coefficient of x² is , the coefficient of x is and the constant term is .
Fill in each blank
Answer:
4.The degree of the polynomial 9x⁵y − 2x⁴y³ + 4y³ is .
Answer:
5.The degree of the polynomial 4x²y − 8x²y² + 5y⁷ is .
Answer:

6.In the polynomial 2x² − 8x + 19, what is the coefficient of x?
- A. −8
- B. 8
- C. 2
- D. 19
Choose the right answer
Answer:
7.The constant term of the polynomial 9x + 13 + 9x² is 13.
True or false?
Answer:
8.The constant term of the polynomial 6x + 16 + 7x² is 6.
True or false?
Answer:
9.In the polynomial 5x² − 8x + 10, what is the coefficient of x?
- A. 5
- B. 8
- C. 10
- D. −8
Choose the right answer
Answer:
10.Write the polynomial 3x² − 2x + 5x³ − 5 in descending powers of x. What do you get?
- A. 5x³ + 3x² − 2x − 5
- B. 5x³ − 2x + 3x² − 5
- C. 5x³ + 3x² + 2x − 5
- D. −5 − 2x + 3x² + 5x³
Choose the right answer
Answer:
11.3x²y³ is a monomial of degree 5.
True or false?
Answer:
12.Which of these is not a polynomial?
- A. x4 + 7
- B. 4x² − 7x
- C. 4x²y − 7
- D. 12
Choose the right answer
Answer:

13.Consider the polynomial 18 − 9x + 9x⁵ − 3x². (a) It has terms; (b) its degree is ; (c) the coefficient of x is .
Fill in each blank
Working:
Answer:
14.Chi-keung wants to write the polynomial 5x − 6x³ + 10 − x² in ascending powers of x. Which is right?
- A. 10 + 5x − 6x³ − x²
- B. −6x³ − x² + 5x + 10
- C. 10 + 5x + x² + 6x³
- D. 10 + 5x − x² − 6x³
Choose the right answer
Working:
Answer:
15.In the polynomial 7x³y + 5x²y³ + 6xy², the coefficient of the term of highest degree is .
Working:
Answer:
16.Which of these is a cubic with three terms (a polynomial of degree 3 with 3 terms)?
- A. 8x² − 9x + 1
- B. 8x³ − 9x + 1
- C. 8x³ − 9x + 1
- D. 8x³ − 9x
Choose the right answer
Working:
Answer:
17.Write the polynomial 4x² − 3x + 9x⁴ − 8 in descending powers of x. Put the terms in order.
- A. −8
- B. 4x²
- C. 9x⁴
- D. −3x
Write the letters in the right order
Working:
Answer:
18.Once simplified, the polynomial 4x² − 9x + 8 − 4x² has degree 2.
True or false?
Working:
Answer:

Show the answers and working

What a polynomial is worksheet: Answers and working

1. 6
6x⁶ has degree 6; 5x²y² has degree 2 + 2 = 4; the constant, 0. A polynomial's degree is its highest term's.
2. 5
4x⁴ has degree 4; 7x²y³ has degree 2 + 3 = 5; the constant, 0. A polynomial's degree is its highest term's.
3. −1, 1, 19
Each sign goes with the term after it: x²'s coefficient is −1; x alone has coefficient 1 and −x has −1, so here it is 1; the constant is 19.
4. 7
Each term's degree is the sum of its indices: 5 + 1 = 6, 4 + 3 = 7, and 3. The highest is the polynomial's.
5. 7
Each term's degree is the sum of its indices: 2 + 1 = 3, 2 + 2 = 4, and 7. The highest is the polynomial's.

6. A. −8
Read the minus as adding a negative: 2x² + (−8x) + 19, so the coefficient of x is −8.
7. True
The constant term is the one with no letter: 13. 9 is the coefficient of x.
8. False
The constant term is the one with no letter: 16. 6 is the coefficient of x.
9. D. −8
Read the minus as adding a negative: 5x² + (−8x) + 10, so the coefficient of x is −8.
10. A. 5x³ + 3x² − 2x − 5
The terms' degrees: 5x³ is 3, 3x² is 2, −2x is 1, −5 is 0. Highest first, each sign moving with its term.
11. True
The degree is the sum of the indices, not the number of letters: 2 + 3 = 5.
12. B. 4x² − 7x
A polynomial never has a letter in a denominator. 7x has x underneath, so 4x² − 7x is not one.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 4, 5, −9
Four terms: 18, −9x, 9x⁵ and −3x². The highest is 9x⁵, so the degree is 5; x's coefficient, sign and all, is −9.
14. D. 10 + 5x − x² − 6x³
The degrees: 10 is 0, 5x is 1, −x² is 2, −6x³ is 3. Lowest first, each sign with its term.
15. 5
The degrees: 3 + 1 = 4, 2 + 3 = 5, 1 + 2 = 3. The highest is 5x²y³, whose coefficient, sign and all, is 5.
16. C. 8x³ − 9x + 1
8x³ − 9x + 1 has three terms, 8x³, −9x and 1, the highest of degree 3.
17. C → B → D → A
Degrees from highest: 9x⁴ is 4, 4x² is 2, −3x is 1, −8 is 0.
18. False
Combine like terms first: 4x² − 4x². If they are equal the x² terms cancel, leaving −9x + 8, of degree 1.

Numsprite · numsprite.com/en/worksheets/polynomials-and-identities/terms-coefficients-and-degree-of-a-polynomial